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Experimental assessment of scale effects affecting two-phase flow properties in hydraulic jumps

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Abstract

A hydraulic jump is the rapid transition from a supercritical to subcritical free-surface flow. It is characterised by strong turbulence and air bubble entrainment. New air–water flow properties were measured in hydraulic jumps with partially developed inflow conditions. The data set together with the earlier data of Chanson (Air bubble entrainment in hydraulic jumps. Similitude and scale effects, 119 p, 2006) yielded similar experiments conducted with identical inflow Froude numbers Fr 1 = 5 and 8.5, but Reynolds numbers between 24,000 and 98,000. The comparative results showed some drastic scale effects in the smaller hydraulic jumps in terms of void fraction, bubble count rate and bubble chord time distributions. The present comparative analysis demonstrated quantitatively that dynamic similarity of two-phase flows in hydraulic jumps cannot be achieved with a Froude similitude. In experimental facilities with Reynolds numbers up to 105, some viscous scale effects were observed in terms of the rate of entrained air and air–water interfacial area.

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Abbreviations

C :

void fraction defined as the volume of air per unit volume of air

C max :

maximum void fraction in the air bubble diffusion layer

D t :

turbulent diffusivity (m2/s) of air bubbles in air–water flow

D* :

dimensionless turbulent diffusivity: \( D^{*} = \frac{{D_{t} }} {{V_{1} d_{1} }} \)

d ab :

bubble size (m)

d 1 :

upstream flow depth (m)

F :

bubble count rate (Hz), or bubble frequency (number of detected air bubbles per unit time)

F max :

maximum bubble count rate (Hz) at a given cross-section

Fr 1 :

upstream Froude number: \( Fr_{1} = V_{1} /{\sqrt {gd_{1} } } \)

g :

gravity constant: g = 9.80 m/s2 in Brisbane, Australia

L scale :

geometric scaling ratio defined as the ratio of prototype to model dimensions

Mo :

Morton number defined as: Mo = g μ4/(ρ σ3)

N ab :

number of air bubbles per record

Q :

water discharge (m3/s)

q :

water discharge per unit width (m2/s)

Re :

Reynolds number: Re = ρV 1 d 1/μ

u′:

root mean square of longitudinal component of turbulent velocity (m/s)

V :

interfacial velocity (m/s)

W :

channel width (m)

We :

Weber number

x :

longitudinal distance from the upstream gate (m)

x 1 :

longitudinal distance from the gate to the jump toe (m)

y :

distance (m) measured normal to the channel bed

\( Y_{{C_{{\max }} }} \) :

distance (m) normal to the jet support where C = C max

z :

transverse distance (m) from the channel centreline

δ:

boundary layer thickness (m)

μ:

dynamic viscosity of water (Pa s)

ρ:

density (kg/m3) of water

σ:

surface tension between air and water (N/m)

∅:

diameter (m)

1:

upstream flow conditions

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Acknowledgments

The writers acknowledge the technical assistance of Graham Illidge and Clive Booth. The first writer acknowledges the financial support of the ESTACA and particularly François Stephan (Head of Department).

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Authors and Affiliations

  1. ESTACA Campus Ouest, Parc Universitaire de Laval - Changé, Rue Georges Charpak, BP 76121, 53061, Laval Cedex 9, France

    Frédéric Murzyn

  2. Division of Civil Engineering, The University of Queensland, Brisbane, QLD, 4072, Australia

    Hubert Chanson

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  1. Frédéric Murzyn
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  2. Hubert Chanson
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Correspondence to Hubert Chanson.

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Murzyn, F., Chanson, H. Experimental assessment of scale effects affecting two-phase flow properties in hydraulic jumps. Exp Fluids 45, 513–521 (2008). https://doi.org/10.1007/s00348-008-0494-4

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  • DOI: https://doi.org/10.1007/s00348-008-0494-4

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